Trigonometric bridge



J. B. HEAVISIDE TRIGONOMETRIC BRIDGE Sept. 8, 1970 Original Filed Feb.25 1965 3 Sheets-Sheet. l

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INVENTOR- JOHN B. HEAVISIDE Mm RM BY W ATTORNEYS Sept. 8, 1970 J. B.HEAVISIDE 3,527,931

TRIGONOMETRIC BRIDGE Original Filed Feb. 25, 1965 3 Sheets-Sheet 2 32 A34 5.; T "u 538 A FlG.' 5

. INVENTOR.

JOHN B. HEAVISIDE FlG.'-4 BY "w, qmb m a, PM;

ATTORNEYS Sept.-8, 1970 J. B. HEAVISIDE 3,527,931

I TRIGONOMETRIC BRIDGE Original Filed Feb. 25, 1965 5 Sheets-Sheet sERIOG! GA/7R 0L INVENTOR. Know! JOHN B. HEAVISIDE BY HW HwW.M 8;

M TGRNEYE? "I-lnited States Patent 3,527,931 TRIGONOMETRIC BRIDGE JohnB. Heaviside, Huntington, N.Y., assignor to North Atlantic Industries,Inc., Plainview, N.Y., a corporation of New York Original applicationFeb. 25, 1965, Ser. No. 435,149, now Patent No. 3,366,804, dated Jan.30, 1968. Divided and this application Jan. 11, 1968, Ser. No. 697,042Int. Cl. G06g 7/22, 7/32 U.S. Cl. 235-479 16 Claims ABSTRACT OF THEDISCLOSURE A computing circuit for processing input complemen- Thisapplication is a division of applicants prior copending application Ser.No. 435,149, filed Feb. 25, 1965, now Pat. 3,366,804, and also includessubject matter described in prior copending application Ser. No. 353,-558, filed Mar. 20, 1964, entitled Data Processing of which applicant isa co-inventor.

This invention relates to switching techniques employed in bridgecircuits and to solid state switching of such arrangements.

Although solid state switching oifers certain advantages overelectro-mechanical arrangements, there are many applications where thesolid state switch, although otherwise acceptable in terms ofcomplexity, cost, and size, does not possess the requisite performancespecifications to meet accuracy requirements.

For example, the dynamic impedance of a solid state diode employed as aswitching element may be several ohms and may be as high as severalhundred ohms. These impedances may be wholly unacceptable in manyapplications.

Although there are means for reducing this dynamic impedance, thesemeans frequently result in an increase in cost and complexity to thepoint where it is more feasible to employ electro-mechanical switchingrrangements.

It is accordingly one object of the invention to provide an improvedsolid state switching arrangement for bridge circuits characterized byan improvement in accuracy which is attained without a correspondingincrease in size or complexity. It is a further object of the inventionto provide improved control arrangements employing such solid stateswitches in combination with bridge circuits for effecting improvementsin various data processing functions including logic operations andbasic computations.

Other objects and advantages of the invention will be set forth in parthereinafter and in part will be obvious herefrom or may be learned bypractice with the invention, the same being realized and attained bymeans of the instrumentalities, combinations and improvements hereinshown, described and claimed.

Serving to illustrate exemplary embodiments of the invention are thedrawings of which:

FIG. 1 is a schematic diagram of a switching arrangement according tothe invention;

FIG. 2 is a schematic wiring diagram of a prior art diode switchingcircuit;

FIG. 3 is a schematic wiring diagram of an inductive divider controlledwith the aid of switching devices such as those illustrated in FIG. 1;

FIG. 4 is a schematic diagram illustrating the switching arrangement ofFIG. 1 in a combination providing an inversion operation;

FIG. 5 is a schematic diagram illustrating the switching techniques ofFIG. 1 in a circuit for converting digital inputs to analogue outputs;and

FIG. 6 is a schematic diagram of a resolver bridge employing switchingtechniques according to the invention.

For the purpose of contrast, initial reference is to the circuit of FIG.2 wherein there is illustrated a solid state diode bridge circuitemployed for switching in accordance with prior art techniques.

The diode bridge is constituted with one branch of seriallyinterconnected diodes D and D and another,

shunt branch, formed of serially connected diodes D and D The cathodeside of the bridge is connected via a resistor R -to switching voltage Esimilarly, the anode side of the bridge is connected via a resistance Rto the switching voltage E The controlled or switched circuit includes asource of potential e having one side connected to the common terminal,illustratively ground, and its other terminal connected to the junctionof D and D The controlled circuit further includes an output or loadcircuit U which may be a utilization device, e.g., some circuit in asignal transmission path. Circuit U has one end connected to thejunction of diodes D and D and its other terminal returned to the returnor ground terminal.

In operation, voltages E E of the proper amplitude and opposite polarityare applied to the switching terminals causing the diodes D D D and D tobecome forwardly biased. As a result conduction is established betweenthe source e and the output circuit U thereby effecting the switchingaction.

A practical circuit of the type shown in FIG. 2 has a number ofsignificant limitations. For one, the resistances R and R act as a loadon the source e. The dynamic impedance of the diodes varies inverselywith the diode current and since the diodes are effectively in serieswith the source and output circuit, it becomes necessary to keep thediode dynamic impedance at a sufliciently low value. To do this it isnecessary to maintain a relatively high current through the diodesthereby necessitata minimization of the size of R and R This, however,as noted above, complicates the loading problem. Hence, the circuitrequires a compromise of diverging criteria with an attendant limitationon performance.

Certain of the disadvantages of FIG. 2 have been overcome by circuitsaccording to the invention such as illustrated in FIG. 1. The mainswitching arrangement therein illustrated includes a diode bridge havingone branch comprising serially interconnected diodes D A and D Thejunction of these two diodes is connected to the common ground terminal.A parallel branch comprises serially interconnected diodes D and D Thejunction of D and D is connected to the circuit to be controlled, U aswell as to the switched voltage source e connected in series with U Inpractice and in certain applications it may be preferable to interchangethe relative positions of source e and switched circuit U In eitherconfiguration, the switching bridge of FIG. 2 provides the common orreference terminal on one side of the bridge (schematically indicatedwith the ground terminal) and the circuit to be switched along with thesource, on the other side of the bridge. Hence, when the bridge isswitched on, the ground connection is supplied to the controlled circuitcausing current flow therein. The ground connection may be by way of animpedance small enough to preclude deterioration in accuracy orinterference with the control circuit. In view of this arrangement, theloading effect on the source provided by the resistors in the switchcontrol circuit is eliminated. Furthermore, the forward switchingvoltage can be low in the circuit of FIG. 1 whereas in the prior artarrangement it must exceed the peak value of the signal source 2.

The anode side of the switching bridge in FIG. 1 is connected to a firstswitching voltage E via a resistance R The anode side is also connectedto a second switching voltage +E via the series combination ofresistance R and the collector-emitter circuit of a transistor driver QOn the cathode side of the diode bridge there is an analogous connectionto a switching voltage +E via a resistance R A and to a second switchingvoltage E via the series combination of resistance R and thecollector-emitter circuit of a driver stage Q The switching voltages +Eand E are operative to back-bias the diode bridge to a sufficient degreeto prevent conduction except under the conditions described hereinafter.In contrast with the arrangement of FIG. 2, the bridge is supplied withseparate switching voltages +E and E which are operative when applied tothe bridge to cause conduction with a resultant switching of the outputcircuit. The voltages :E may be relatively small compared with theamplitude of E and in an illustrative application E may be in the orderof three volts while E is thirty volts The base of Q is connected via aresistance R and a diode D to an input terminal 1 Similarly, the base ofQ is connected via the series combination of R and D to terminal 1 Withthe circuit as thus far described, the application of a potential at 1which is sulficient to forwardly bias Q A will cause the saturation of Qand the resultant connection of the on voltage, E to the diode bridgevia resistance R A similar voltage of opposite polarity applied toterminal 1 causes Q to be switched on with the result that +E is appliedto the anode side of the bridge via R When these actions areaccomplished, the bridge is rendered conductive, causing the switchingcircuit U 2, to be grounded and therefore completed.

It should be noted here that Q, and Q are transistors of complementarytypes and are biased by E and +E such that a voltage positive withrespect to E (e.g., a ground or voltage of zero amplitude) can switch onQ while a voltage negative relative to +E which again can be the groundpotential, can cause the switching on of Q Alternatively, by properselection of bias, base resistances and switching voltages, theswitching levels for the A and B circuits can be made dilferent to adaptthe arrangement to logic operations employing multi-switching levels.

Since the forward switching voltage 1E may be comparatively low andsince the resistances R and R do not load the switched circuit and thusmay be of low value, there is less power required for switching a givenamount of output power.

The circuit of FIG. 1 is amenable to a latching or memory typecharacteristic and to this end cross coupling circuits G and G may beemployed, the former connecting the collector of Q A to input terminal Ivia a switch 8,, and the latter connecting the collector of Q to inputterminal 1 via a switch S Assuming both switches 5,, S are closed, thecircuit of FIG. 1 will latch on if a ground or other suitable potentialis applied to either of the input terminals 1,, or I In the absence ofsuch a potential the circuit is maintained ofi because the collector ofQ is negative relative to the potential E while the collector of Q ismore positive than the potential +E Once the circuit has been switchedon (and assuming of course that switches S, and S are closed), thecircuit will stay in a conductive state even after the switching voltageis removed from terminal 1 or I This results from the relativelynegative potential which is coupled from the collector of Q, to the baseof Q and because of the relatively positive potential which is coupledfrom the collector of Q to the base of Q In certain applications it isdesirable to have the capability of effecting switching at differentcontrol levels. This is accomplished in FIG. 1 by simply opening switchS or S When this is done the latching characteristic is eliminated but achoice of switching levels is made available. For example, and assumingthat switch S is open, a relatively negative potential applied at inputterminal 1 causes Q to be switched on. When this occurs a forwardbiasing potential is coupled from the collector of Q to the base of Q sothat the entire bridge is switched on. If on the other hand S is closedand S is opened, a relatively positive potential at terminal 1 willswitch the bridge into conduction.

The circuit of FIG. 1 is also particularly adapted to supply amonitoring signal or an auxiliary signal and this is advantageouslyattained from any one of several points including the junction A of FIG.1 to which is connected an auxiliary output terminal M useful formonitoring or other purposes.

Because of its performance characteristics and in view of the fact thatit acts to complete a circuit to ground, the embodiment of FIG. 1 isalso adapted to provide multi-pole operation. This is readilyaccomplished by connecting additional branches in parallel with the mainbridge. Thus, as illustrated, an additional branch comprising serialdiodes D and D may be connected in parallel with the bridge with thejunction of D and D being connected to the switched circuit U and itsseries source e. Similarly, an additional circuit U and its source 2 maybe switched by connecting the same to the junction in an additionalbranch comprising serially connected diodes D and D The diodes D and Din the base circuits of Q and Q respectively, serve the function ofpreventing damage to the associated collector-base junction. In additionthese diodes may-be employed in combination with parallel input diodesto provide logic operations, for example, OR functions. Thus asillustrated in FIG. 1, the input 1 may be paralled by inputs I and Iconnected to R via respective diodes D and D The driver sections of FIG.1 may thus be utilized to provide logic operations, a technique which isfrequently not feasible in electro-mechanical relay circuits.

Because of its accuracy, the switching arrangement of FIG. 1 isparticularly adapted for use in certain computing operations where highorder accuracy is required. However, the switching device according tothe invention functions to complete the ground circuit and for thisreason its combination with other computation elements in some casesrequires certain unique circuit configurations, certain of thesearrangements are illustrated in FIGS. 3, 4, 5 and 6.

Illustrated in FIG. 3 is an inductive divider such as used in dataprocessing, e.g., in precision ratiometric measurement of AC voltages.The divider comprises a transformer T having a plurality of spacedwinding taps connected to define individual winding sections, W W W W Inthe illustration, the complete winding is of the decade type and eachsection has its tap connected to a respective switching circuit S S SThese switching circuits are as illustrated in FIG. 1 (with theadditional switching circuits D D and D D not utilized). The outputterminal of each of the switching circuits S S S is connected to groundsuch that the application of a suitable voltage to the respectivecontrol terminal 1 I I I connects the tap associated therewith toground. This tap grounding action is different from the usual tapselection arrangements found in inductive dividers and to make thisaction effective, the upper terminal of the divider is connected to thesucceeding circuit C which may comprise an output or additionalinterpolating windings on the same or a different core. The inputvoltage is applied to terminals I and I connected across the entiredivider.

It may be seen that the closure of any of the switches S S S byapplication of an onsignal at the respective terminal I I I results in agrounding of the corresponding tap with the result that all sectionsbelow that point do not make any contribution to the resultant outputwhich is developed across the taps above that point and which isconnected with the output circuit 0C. The switches will each have anappropriate one of the cross couplings G or G conductive so that theappropriate polarity voltage will cause switch on while the oppositecauses switch of). However, with certain logic circuits it may bepreferable to employ the switches with their latching characteristic.

For accomplishing inversion functions with the switch of FIG. 1 circuitsmay be employed such as illustrated in FIG. 4. As seen therein atransformer T has the two outside tenminals of its primary connected toground via respective switches S and S of the type such as shown in FIG.1 with one switch, e.g., S having the cross circuit G complete while Shas the opposite coupling G completed. The center tap of the primarywinding, W is connected to the signal source, e, the other terminalwhich is grounded. The transformer secondary comprises a winding Whaving output terminals I and I A signal voltage e of selected polarityis applied to the control terrnins I I of the switches.

It may be seen that the transformer will execute a phase reversal whenthe states of switches S and S are reversed. Thus, with S on and S ofi,e.g., as will occur when signal voltage e is positive, the outputvoltage at terminal I is out of phase with the voltage e. When S isswitched on and S switched of), the voltage e and the output voltage atI are in phase.

The switching circuits according to the invention are adapted to performcertain binary-digital conversion techniques, one of which isillustrated in FIG. 5. The circuit therein converts a digital inputapplied at terminals B B B and B into a corresponding analogue voltage,e which appears at output terminal I In implementing the foregoing, avoltage e is applied via a terminal I to the primary winding of atransformer T The transformer secondary is tapped and supplies properlyweighted proportions of the voltage e to each of the four summingbranches of the converter. A first branch comprises the serialcombination of resistance R and switch S this branch is connected to thetop of the transformer secondary. Receiving a reduced potential is thesimilar series branch comprising resistor R and switching cicuit SSuccessively lower potentials are applied to the third and fourthbranches comprising R34/S34 and Rug/S33.

Although proper weighting of the inputs may be accomplished by anappropriate proportioning of the resistors R31, R32, R and R there is anadvantage in weighting the voltages prior to application to therespective branches. In this arrangement the resistors R R32, R and Rmay be all of the same size so that with their respective straycapacitances, the phase shift in each branch is substantially equal.

The output sides of the branches are all connected together at a summingjunction SI of an amplifier A Across the amplifier is feedback resistorR while the amplifier output is connected to output terminal I Theswitches S 1, S32, S and S are controlled according to the digitalinputs supplied at respective control terminals B B B and B By switchingthe switching circuits an individually and in suitable combinations,various net digital states of the amplifier can be established andproportional analogue voltages thereby developed at the output terminal.For example a switching signal on terminals B and B representing thequantity 10 for example, will cause the respective switches S and S tobe switched on. As a consequence the branches containing R and R areconnected to the summing junction SI with the effect that the amplifierhas a gain proportional to the illustrated digital input of 10. When Band B are energized, the corresponding branches R and R are renderedeffective so that the amplifier in eifect provides a sum proportional tothe digital input (5), i.e., provides a corresponding analogue voltagewhich appears at the output. It may be noted that the low switchingimpedance of the switching circuits S S S and S is especiallyadvantageous in the circuit of FIG. 5 where the switch outputs areconnected to the virtual ground of the summing junction with theirnegligible impedances inserted in each of the summing branches in serieswith the input resistors.

In FIG. 6 there is illustrated a resolver bridge system employing theswitching arrangements according to the invention including the phaseinversion technique as illustrated in FIG. 4 and the inductive dividerswitching technique shown in FIG. 3. In general organization the bridgesystem of FIG. 6 is similar to that disclosed in copending application,Ser. No. 353,558, filed Mar. 20, 1964 Computer Circuits for PROCESSINGtrigonometric Data, of which the applicant is co-inventor and which isassigned to the assignee of the instant application.

The input of FIG. 6 comprises the resolver voltages 2 and e the formerrepresenting the sine component and the latter the cosine component.These voltages may initially be in the form of synchro data which areconverted to resolver form by way of the converted DC Examples of suchconverters are illustrated and described in the above-mentionedcopending application. Alternatively, the data may be of resolver typein origin.

Voltage e is applied to the primary winding of a transformer T whilevoltage e is similarly applied to the primary of a transformer T Thevoltages are each applied to the center tap of the respective primaryand the outside terminals of both windings are provided with solid stateswitches such as those described and illustrated in FIG. 1. It may beseen that the primary of each transformer is instrumented to effectphase reversal in accordance with the switching of the switch pairs S /Sin the case of T and Sqo/Sq in the case of transformer T These switchesare actuated by electrical signals generated by the bridge adjust,following the reversal techniques described in the aforesaid copendingapplication.

The secondary of transformer T consists of two separate inductivedividers each tapped to yield values of sine/ cosine increments, D, of10 degrees. It should of course be understood that other increments maybe used. Each tap is connected to a respective switch of the typeillustrated in FIG. 1 with the switch functioning to ground therespective tap when the switch is rendered conductive by the appropriatecontrol signal. This arrangement is symbolized by the block labeled SCone of the switches being schematically indicated in the closed statewhereupon its associated tap connection is grounded. A similararrangement characterizes the switching circuits connected to thewinding W of T this being shown schematically by the block labeled S0The switching of the circuits in SC and SC are coordinated such that theadjustment of the bridge to an angle 04 causes that tap to be selectedin SC which yields the sine of a at the output terminal of W and causesthat tap to be selected in SO which yields at the output terminal of Wthe sine of (cq-i-D). Of course it should be borne in mind that theoutputs from both windings are multiplied by a voltage related to cosine0.

A similar arrangement characterizes the two secondary windings W and Wof transformer T The switching in S0 is such that the output includesthe factor cosine a while the switching in SO yields the cosine of(ct-I-D).

The value of D in degrees is the same as the size of each dividerincrement.

The resultant four outputs are applied to combining means embodied as atransformer T and a transformer T The primary winding W of transformer Tis energized by the combination of signals appearing at the outputs ofwindings W and W The primary winding W of transformer T is energized bythe combination of signals developed at windings W and W This computingoperation is similar to that described in the aforesaid copendingapplication.

The output signals developed across the secondaries of transformers Tand T are combined in the manner shown with one terminal of W and thecenter tap of W being connected across an inductive divider D The otherend terminal of W and one end terminal of W are connected together whilethe other end terminal of W is connected via a resistance R to thecommon switched terminals of a plurality of solid state switches, SCeach of which is connected to a respective tap on D The junction ofresistance R and this common terminal is connected to a null detectorwhich is responsive to the condition of balance or unbalance in thebridge. Divider D and the associated switches SC function as aninterpolating arrangement for interpolating the relatively coarseadjustment of the bridge at the input dividers T and T The adjustment ofswitches in SC is coordinated with the adjustment of the switching net-WOlkS S061, SC62, SCH and S072.

The voltage e across W is combined with e across W In the illustratedcase e is substracted from e and the resultant voltage e applied to thedivider to produce a fraction of e i.e., a net signal ke,.

The output circuit of FIG. 6 is in essence a form of summing circuitsuch as shown in FIG. in which currents are summed. The current flowingthrough R is a function of 2 While the current flowing out of the switchnetwork is a function of k2,. The summing junction is effectively at aground potential because of the feedback effect involving the wholebridge.

The bridge may be of the automatic type as described in the aforesaidcopending application, i.e., with the bridge adjustment controlled byway of feedback from the null detector or with the bridge adjustmenteffected independently thereof with the null detector employed toprovide read-out or storage of that adjustment angle which yields anull. Alternatively the bridge may be completely manual with the nulldetector isolated from the bridge adjust and read-out circuits.

The invention is not limited to the specific mechanisms shown anddescribed since modifications will undoubtedly occur to those skilled inthe art. Changes may be made within the scope of the accompanying claimsWithout departing from the spirit and chief advantages of the invention.

What is claimed is:

1. A trigonometric bridge for processing first and second complementaryinput trigonometric functions defined by amplitude and angular datacomprising:

bridge adjust means for providing first and second complementaryadjusting functions;

first and second computing means each having taps and each includingswitching means, for producing product functions of said inputtrigonometric functions and said adjusting functions,

said first and second computing means being respectively operablyconnected to and energized by said first and second input trigonometricfunctions. said first and second computing means being operablyconnected to said bridge adjust means for respectively selectivelygrounding said taps of said first and second computing means by saidswitching means in accordance with said first and second adjustingfunctions for producing as outputs said product functions; interpolatingmeans operably connected to said computing means and responsive to saidoutput product functions for deriving a first signal proportional tosaid amplitude data; and means operably connected to said interpolatingmeans and to said computing means and responsive to said first signaland to said output product functions for developing an indication ofsaid angular data.

2. A bridge according to claim 1 in which said means connected to saidinterpolating means and said computing means includes null detectormeans responsive to said interpolating means and having a virtual groundpoint, and

said interpolating means comprise a tapped divider having third switchmeans coupled between said taps and said virtual ground point.

3. A bridge according to claim 1 in which said interpolating meanscompridse a compensated interpolator.

4. A trigonometric bridge for processing first and second complementaryinput trigonometric functions defined by amplitude data and angular data0 comprising;

bridge adjust means for providing first and second complementaryadjusting functions of angular data at;

first and second computing means each having taps and each includingswitching means, for producing product functions of said inputtrigonometric functions of 0 and said adjusting functions of a,

said first and second computing means being respectively operablyconnected to and energized by said first and second input trigonometricfunctions of 0, said first and second computing means being operablyconnected to said bridge adjust means for respectively selectivelygrounding said taps of said first and second computing means by saidswitching means in accordance with said first and second adjustingfunctions of a for producing as output said product functions; meansoperably connected to said first and second computing means andresponsive to said output product functions for deriving a first signalwhich is a function of (0-0) and said amplitude data of said functionsof 0 but is independent of the individual magnitudes of 6 and a, andderiving a second signal which is approximately proportional to saidamplitude data; and combining means responsive to said derived signalsfor computing the value of said derived signals to compute (0a) andthereby obtain an output indicative of 0.

5. A bridge as defined in claim 4 in which said combining means includeratio computing means having taps and ground switching means foradjusting said ratio computing means in accordance with a function of(0a).

6. A bridge as defined in claim 5 in which said ground switching meanscomprise diode bridge means; said diode bridge means comprising twodiagonal signal junctions, one of which is grounded and the other ofwhich is connected to said respective tap of said ratio computing means,a control circuit interconnecting diagonally opposite control junctionsof said diode bridge for turning the bridge on and off, a forwardbiasing potential source in said control circuit having one terminalconnected to ground, and means in said control circuit for effectivelyconnecting said forward biasing source to said diode bridge to turn sameon for grounding said tap.

7. A bridge as defined in claim 4 in which said first and secondcomputing means comprise trigonometric ratio dividers;

said means for deriving said first signal comprise summing means.

'8. A trigonometric bridge for processing first and second complementaryinput trigonometric functions defined by amplitude and angular datacomprising:

bridge adjust means for providing first and second complementaryadjusting functions;

first and second computing means each having taps and each includingswitching means, for producing product functions of said inputtrigonometric functions and said adjusting functions,

said first and second computing means being respectively operablyconnected to and energized by said first and second input trigonometricfunctions, said first and second computing means being operablyconnected to said bridge adjust means for respectively selectivelygrounding said taps of said first and second computing means by saidswitching means in accordance with said first and second adjustingfunctions for producing as outputs said product functions; interpolatingmeans operably connected to said computing means and responsive to saidoutput product functions for deriving a first signal proportional tosaid amplitude data;

null detecting means operably connected to said interpolating means andto said computing means and responsive to said output product functionsand said first signal for developing an indication of said angular data;and

feedback control means operably connecting said null detecting means andsaid bridge adjust means for altering said first and second adjustingfunctions in accordance with said indication.

9. A bridge as defined in claim 8 in which said null detector means hasa virtual ground point,

and

said interpolating means comprise a tapped divider having third switchmeans coupled between said taps and said virtual ground point. 10. Abridge as defined in claim 8 in which said tapped computing means eachcomprise trigonometric inductive dividers tapped to provide a pluralityof sine/ cosine values corresponding to a set of adjustment angles.

11. A bridge as defined in claim 8 in which said interpolating meanscomprise a compensated interpolator.

12. A bridge as defined in claim 8 in which said switching meanscomprise diode bridge means; said diode bridge means comprising twodiagonal signal junctions one of which is grounded and the other ofwhich is connected to the respective tap of the respective computingmeans, a control circuit interconnecting diagonally opposite controljunctions of said diode bridge for turning the bridge on and off, aforward biasing potential source in said control circuit having oneterminal connected to ground, and means in said control circuit foreffectively connecting said forward biasing source to said diode bridgeto turn same on for grounding said tap.

13.. A trigonometric bridge for processing first and secondcomplementary input trigonometric functions defined by amplitude dataand angular data comprising: bridge adjust means for providing first andSecond com plementary adjusting functions of angular data a;

first and second computing means each having taps and each includingswitching means, for producing product functions of said inputtrigonometric functions of 0 and said adjusting functions of 0:.

said first and second computing means being respectively operablyconnected to and energized by said first and second input trigonometricfunctions of 0,

said first and second computing means being operably connected to saidbridge adjust means for respectively selectively grounding said taps ofsaid first and second computing means by said switching means inaccordance with said first and second adjusting functions of a forproducing as outputs said product functions;

means operably connected to said first and second computing means andresponsive to said products for deriving a first signal which is afunction of (0u) and said amplitude data of said first and secondfunctions of 0 but is independent of the individual magnitudes of 0 anda; and deriving a second signal which is approximately proportioned tosaid amplitude data; and combining means responsive to said derivedsignals for computing the value of said derived signals to compute (0a)and thereby obtain an output indicative of 0; and feedback control meansoperably connected to said combining means and said bridge adjust meansfor altering said first and second adjusting functions of oz inaccordance with said output.

14. A bridge as defined in claim 13 in which said first and secondcomputing means comprise trigonometric ratio dividers;

said means for deriving a first signal comprise summing means; and

said combining means are connected to be responsive to said summingmeans for computing (0-a).

15. A bridge as defined in claim 13 in which said combining meansinclude ratio computing means and ground switching means for adjustingsaid ratio computing means in accordance with a function of (0a) tocompute said ratio.

16. A bridge as defined in claim 13 in which said switchin gmeanscomprise diode bridge means; said diode bridge means comprising twodiagonal signal junctions one of which is grounded and the other ofwhich is connected to the respective tap of the respective computingmeans, a control circuit interconnecting diagonally opposite controljunctions of said diode bridge for turning the bridge on and off, aforward biasing potential source in said control circuit having oneterminal connected to ground, and means in said control circuit forefiectively connecting said forward biasing source to said diode bridgeto turn same on for grounding said tap.

References Cited UNITED STATES PATENTS 3,071,324 1/1963 Schroeder et al.235186 X 3,205,492 9/1965 Young et a1. 340-347 3,277,461 10/ 1966 Selvin340-347 EUGENE G. BOTZ, Primary Examiner F. D. GRUBER, AssistantExaminer US. Cl. X.R. 235-186, 32344.5

